No, that's not how the new EU legislation works. The new laws build off existing Digital Services Act (DSA) and legacy E-Commerce Directive (2000/31/EC) requirements. The DSA states again that you would have to lock down access to the material (once you become aware) and then inform authorities.
All site operators maintain safe harbor with EU authorities unless those two points are broken. In both US and EU pending legislation, no requirement to scan all STLs is required, so you do not have to automatically check all files like you mentioned.